Problem: Rewrite as a simplified fraction. ${2.2\overline{80} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2280.808...\\ 10x &= 22.808...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2258}$ ${x = \dfrac{2258}{990}} $ ${x = \dfrac{1129}{495}} \text{or} {2 \dfrac{139}{495}}$